The inverse problem can be solved to reconstruct electrical activity inside a body surface based measured electrical activity on the body surface. One example of such an application relates to electrocardiographic imaging where electrical potentials measured on a torso can be combined with geometry information to reconstruct electrical potentials on a cardiac surface. For example, a computer can combine and process the body surface electrical potentials activity data and the geometry data to reconstruct estimates of the cardiac surface potentials (e.g., epicardial potentials). The reconstructed cardiac surface potentials may in turn be processed to generate appropriate epicardial cardiac surface potential maps, epicardial cardiac surface electrograms, and epicardial cardiac surface isochrones.